Manipulation of drops with electrowetting:
From morphological transitions to microfluidics
Manipulation of drops with electrowetting:
From morphological transitions to microfluidics
Riëlle de Ruiter
Prof. dr. ir. J.W.M. Hilgenkamp University of Twente, chairman Prof. dr. F. Mugele University of Twente, promotor Dr. M.H.G. Duits University of Twente, assistant promotor Prof. D. Quéré ESPCI ParisTech Prof. K.K. Varanasi Massachusetts Institute of Technology Prof. W.T.S. Huck Radboud University Nijmegen Dr. I.R. Collins BP Prof. dr. A. van den Berg University of Twente Prof. dr. R.G.H. Lammertink University of Twente The research described in this thesis was performed at the Physics of Complex Fluids group within the MESA+ Institute for Nanotechnology and the Department of Science and Technology of the University of Twente. This work is part of the ExploRe research program which is financially supported by BP plc. Title: Manipulation of drops with electrowetting: From morphological transitions to microfluidics Author: Riëlle de Ruiter ISBN: 978‐90‐365‐3639‐4 DOI: 10.3990/1.9789036536394 Copyright © 2014 by Riëlle de Ruiter, Enschede, the Netherlands. All rights reserved. No part of this work may be reproduced by print, photocopy, or any other means without prior permission in writing of the author. Printed by Gildeprint Drukkerijen, Enschede.
MANIPULATION OF DROPS WITH ELECTROWETTING: FROM MORPHOLOGICAL TRANSITIONS TO MICROFLUIDICS PROEFSCHRIFT ter verkrijging van de graad doctor aan de Universiteit Twente, op gezag van de rector magnificus, prof. dr. H. Brinksma, volgens besluit van het College voor Promoties in het openbaar te verdedigen op woensdag 26 maart 2014 om 14:15 uur door Riëlle de Ruiter geboren op 5 april 1985 te Tiel
Promotor: Prof. dr. Frieder Mugele Assistant promotor: Dr. Michèl Duits
Table of contents
Table of contents v Summary vii Samenvatting ix 1 Introduction 1 1.1 Motivation: Enhanced Oil Recovery 2 1.2 Thesis outline 7 2 Scientific background 13 2.1 Basic principles of capillarity and wetting 14 2.2 Wetting of microscopically textured surfaces 20 2.3 Morphological transitions 23 2.4 Some examples of morphological transitions 28 2.5 Modifying wettability via electrowetting 33 3 Influence of cationic composition and pH on the formation of metal stearates at oil‐ water interfaces 41 3.1 Introduction 42 3.2 Materials and methods 44 3.3 Results 47 3.4 Discussion and interpretation 58 3.5 Conclusions and outlook 61 4 Use of electrowetting to measure dynamic interfacial tensions of a microdrop 69 4.1 Introduction 70 4.2 Materials and methods 71 4.3 Results and discussion 73 4.4 Conclusions 775 Influence of contact angle hysteresis on the morphology of drops confined between a sphere and a plane 81 5.1 Introduction 82 5.2 Materials and methods 84 5.3 Results 86 5.4 Discussion 90 5.5 Conclusion 95 6 Buoyant droplets on functional fibers 103 6.1 Introduction 104 6.2 Materials and methods 106 6.3 Results 109 6.4 Discussion 114 7 Electrostatic potential wells for on‐demand drop manipulation in microchannels 121 7.1 Introduction 122 7.2 Materials and methods 124 7.3 Principles of on‐demand trapping and release 126 7.4 Applications 133 7.5 Conclusions 137 8 Concluding remarks 147 8.1 Morphological transitions 148 8.2 Micropatterned surfaces 150 8.3 Role of the oil‐water interface 150 Acknowledgements 153 List of publications 155 About the author 159
Summary
In spite of today’s growing efforts to exploit alternative sources of energy, fossil fuels are still expected to serve an important part of the energy demand of society, at least for the next decades. Recovery of the oil is a technologically challenging problem. Crude oil is typically trapped in the narrow regions between the grains of a sedimentary rock at a depth of several kilometers underground. During recovery, the injected water and the released oil need to flow through interconnected pores with sizes that vary from the submicron to submillimeter range. Oil recovery can thus be considered as an applied two‐ phase flow microfluidics problem. With the current technology only about 50% of the oil present in the pore space can be recovered. The other part remains in the reservoir due to heterogeneity in the wettability and structure of the rock. In this thesis we address various scientific aspects related to the mobilization and subsequent removal of small liquid volumes interacting with heterogeneous solid walls. In Enhanced Oil Recovery, the low salinity water flooding method is thought to improve oil recovery via a wettability alteration of the rock. However, the composition of the injection water also influences the adsorption of amphiphilic species onto the oil‐water interface. In Chapter 3 we study this interfacial adsorption and assembly for a model system of decane containing stearic acid, in contact with an aqueous phase. Deprotonation, adsorption and molecular rearrangement precede the formation of solid metal stearate multilayers. Their formation and final composition strongly depend on the pH and cationic composition of the aqueous phase. Layer formation is facilitated by synergistic effects of simultaneously present mono‐ and divalent cations. We find that Ca2+ is preferentially incorporated in the final layers. The formation of solid layers with a surface viscoelasticity – which is more pronounced in the presence of divalent ions – might influence the release of drops in complex natural systems. Further study of these systems may be justified by more concrete evidence that these layers play an important role under reservoir conditions, i.e., elevated temperatures and the presence of multiple interfacially active species.Oil drops in the rock pore space are in contact with chemically and topographically heterogeneous surfaces. As a consequence, a drop is situated in an energy landscape with various local minimum energy configurations separated by energy barriers. Variation of the drop volume or surface wettability will change this landscape and may cause displacements and/ or morphology changes of the drop. In low salinity water flooding, desorption of organic compounds is supposed to change the wettability of the rock. In this
thesis however, we use electrowetting as a method to tune the wettability of substrates reversibly and on very short time scales, and investigate the morphological transitions in two different model systems. In Chapter 5 we first discuss the case of a drop confined between a sphere and a plane as a generic geometry representing a pore throat. The radial position of the drop with respect to the symmetry axis is studied for its dependence on the contact angle, drop volume, and sphere/ plane separation distance. Analysis of numerically calculated energy curves shows a continuous and reversible radially in‐ and outward movement upon variations in the contact angle. However, due to the small driving forces, for non‐ideal surfaces with chemical or topographic heterogeneity, pinning forces can drastically affect the drop behavior. A substantial history‐dependence in the shape and position of the drop can then occur, and the outward movement can even become discontinuous.
In contrast, transitions of a drop in contact with a cylindrical substrate, i.e., a fiber, are always discontinuous. Depending on drop volume and wettability, the drop can either attain a barrel morphology engulfing the fiber, or a clamshell morphology sitting on the side of the fiber. In Chapter 6 we specifically investigate the effect of an external driving force, in this case buoyancy, on the instability lines. The introduction of gravitational forces shrinks the bistable and barrel regimes in favor of the clamshell regime. More importantly, at large drop volumes a new stability limit related to (partial) detachment of the drop from the fiber is found for the clamshell morphology. The typical drop size for detachment increases with the capillary length of the system.
In oil recovery, the gravity forces on a drop are generally too small to be of importance. However, (abrupt) changes in drop shape and position may also affect the drag force exerted by the surrounding fluid. In Chapter 7 we consider the balance between retaining and driving forces on drops confined between the top and bottom walls of a microfluidic channel. Electrodes are incorporated in the microchannel wall to create a local (electro)wetting defect with tunable strength. A simple model comparing the maximum trapping force and the drag force provides excellent predictions about whether a drop is released from a pinning site.
In addition, the tunable electrical traps can be used as a new tool in continuous‐flow microfluidics. Combining the individual drop control achieved using electrical actuation with the high throughput of channel‐based microfluidics enables several drop manipulations that are important for many lab‐on‐a‐chip applications, such as on‐demand drop trapping and release, guiding, and high‐speed sorting.
Samenvatting
Ondanks toenemende inspanningen om alternatieve energiebronnen te benutten, is het de verwachting dat fossiele brandstoffen in ieder geval in de aankomende decennia nog een belangrijk aandeel zullen leveren aan de globale energievoorziening. Oliewinning is technologisch gezien nog altijd een uitdaging. Ruwe olie zit opgesloten in de nauwe poriën van korrelig sedimentair gesteente op een diepte van enkele kilometers onder de grond. Tijdens oliewinning stromen injectiewater en de losgemaakte olie door een netwerk van poriën met groottes die variëren van het submicrometer tot submillimeter gebied. Oliewinning kan dus beschouwd worden als een toegepast twee‐fase stromingsprobleem op microfluïdische schaal. Met de huidige winningstechnieken kan maar ongeveer 50% van de totale hoeveelheid olie die aanwezig is in de porieruimte gewonnen worden. Het andere deel blijft achter in het reservoir ten gevolge van heterogeniteit in de bevochtigingseigenschappen en structuur van het gesteente. In dit proefschrift behandelen we een aantal wetenschappelijke aspecten die gerelateerd zijn aan de mobilisatie en verwijdering van kleine vloeistofvolumes die een interactie hebben met een heterogene vaste wand.Tijdens ‘Enhanced Oil Recovery’ wordt het injecteren van (zee)water met een verlaagd zoutgehalte verondersteld de oliewinning te verhogen door veranderingen in de bevochtigingseigenschappen van het gesteente. De samenstelling van het injectiewater beïnvloedt echter ook de adsorptie van amfifiele moleculen aan het olie‐water grensvlak. In Hoofdstuk 3 bestuderen we deze adsorptie en de daaropvolgende reorganisatie van moleculen voor een modelsysteem bestaande uit een oplossing van stearinezuur in decaan, in contact met een waterfase. Deprotonatie, adsorptie, en moleculaire herschikkingen gaan vooraf aan de vorming van vaste multilagen van metaalstearaten. De vorming en de uiteindelijke samenstelling hiervan zijn sterk afhankelijk van de zuurgraad en de samenstelling van de kationen in de waterfase. Laagvorming wordt versterk door synergetische effecten van gelijktijdig aanwezige mono‐ en divalente kationen. We zien dat bij voorkeur Ca2+ in de uiteindelijke laag wordt opgenomen. De vorming van vaste lagen met een oppervlakte‐visco‐elasticiteit – die in aanwezigheid van divalente ionen meer uitgesproken is – kan het loslaten van druppels in complexe natuurlijke systemen beïnvloeden. Een vervolgstudie is gerechtvaardigd indien er meer concreet bewijs is dat deze lagen een belangrijke rol spelen onder de omstandigheden zoals die in oliereservoirs heersen, met name een hogere temperatuur en de aanwezigheid van een verscheidenheid aan oppervlakte‐actieve stoffen.
Oliedruppels in de porieruimte van gesteente bevinden zich in contact met chemisch heterogene en onregelmatig gevormde oppervlakken. Al gevolg hiervan bevindt een druppel zich in een energielandschap met verschillende lokale minimum‐energie configuraties die gescheiden zijn door activeringsenergieën. Een variatie in het druppelvolume of de bevochtigingseigenschappen van het gesteente zal dit landschap doen veranderen en mogelijk een verplaatsing en/ of verandering in morfologie van de druppel veroorzaken. Tijdens het injecteren van water met een verlaagd zoutgehalte worden veranderingen in de bevochtigingseigenschappen vermoedelijk veroorzaakt door desorptie van organische componenten. In dit proefschrift gebruiken we echter ‘electrowetting’ om de bevochtigingseigenschappen van substraten omkeerbaar en op zeer korte tijdschalen aan te passen, en onderzoeken we morfologische overgangen in twee verschillende modelsystemen. In Hoofdstuk 5 behandelen we eerst het geval van een druppel in de ruimte tussen een bol en een vlakke plaat; dit is een simpel model voor een porieruimte tussen twee korrels. We onderzoeken op welke manier de radiale positie van de druppel ten opzichte van de symmetrieas afhangt van de contacthoek, het druppelvolume, en de afstand tussen de bol en de plaat. Een analyse van de numeriek bepaalde energiecurven toont een continue en omkeerbare radiale beweging naar binnen en buiten wanneer veranderingen worden aangebracht in de contacthoek. Doordat de bijbehorende drijvende krachten klein zijn kunnen plakkrachten het druppelgedrag op niet‐ideale oppervlakken met chemische heterogeniteit of ruwheid echter drastisch veranderen. Het is dan mogelijk dat de vorm en positie van de druppel sterk afhankelijk worden van de voorgeschiedenis, en de beweging naar buiten kan zelfs een discontinuïteit vertonen.
Transities van een druppel in contact met een cylindrisch substraat, een vezel, zijn echter altijd discontinu. De druppel vormt afhankelijk van het druppelvolume en de bevochtigingseigenschappen ofwel een zogenaamde ‘barrel’ die de gehele vezel omringt, ofwel een ‘clamshell’ die aan één kant van de vezel zit. In Hoofdstuk 6 onderzoeken we specifiek het effect van een externe drijvende kracht, in dit geval de Archimedeskracht op de instabiliteitslijnen. De introductie van gravitatiekrachten verkleint de bistabiliteits‐ en barrelregimes in het voordeel van het clamshellregime. Van groter belang is de nieuwe stabiliteitslimiet die wordt gevonden voor de clamshell: voor grote druppelvolumes laat (een gedeelte van) de druppel los van de vezel. De kenmerkende druppelgrootte voor loslating neemt toe met de capillaire lengte van het systeem.
In oliewinning zijn de gravitatiekrachten op druppels over het algemeen te klein om van belang te zijn. Veranderingen in de druppelvorm en ‐positie kunnen echter ook effect
Samenvatting xi
hebben op de weerstandskracht die wordt uitgeoefend door de omringende vloeistof. In
Hoofdstuk 7 beschouwen we de balans tussen de weerhoudende en drijvende krachten
op druppels die tussen de boven‐ en onderwand van een microfluïdisch kanaal ingeklemd zitten. Electroden worden in de wand van het kanaal ingebed om een lokaal (electro)wetting defect met instelbare sterkte te maken. Een eenvoudig model dat de maximale ‘plakkracht’ en de weerstandskracht vergelijkt, levert voortreffelijke voorspellingen of een druppel wordt losgemaakt van het defect op.
De instelbare elektrostatische energieputten kunnen daarnaast gebruikt worden voor controle over individuele druppels in microfluïdische systemen met een continue stroming. Het combineren van manipulatie van individuele druppels op (elektrisch gestuurd) commando, met de grote verwerkingscapaciteit van microfluïdische systemen met een continue stroming maakt verschillende druppelmanoeuvres mogelijk die belangrijk zijn voor vele lab‐on‐a‐chip toepassingen, zoals het gecontroleerd vasthouden en loslaten van druppels, loodsen, en sorteren op hoge snelheid.
Chapter 1
Introduction
The main motivation for this thesis originates from scientific challenges in Enhanced Oil Recovery (EOR). Developing new technologies for increasing the recovery from known reservoirs is becoming more important due to the sustained high demand for oil, combined with the difficulties in finding new reserves through exploration. An example of a novel EOR technique is low salinity water flooding, where wettability alteration is thought to be responsible for the mobilization of oil interacting with clay‐covered rock surfaces. While the success of this approach has been demonstrated in many cases, questions remain about the precise mechanism and the scope of the method. Scientific studies are for example necessary to unravel the exact physical‐chemical mechanisms of wettability alteration, to investigate the universality with respect to rock and clay types, and to determine the local and/ or global wettability changes associated with a certain increase in recovery. In this thesis we address various aspects related to the mobilization and subsequent release of small liquid volumes interacting with solid walls. This chapter starts with a concise overview of (enhanced) oil recovery, in particular low salinity water flooding, and is concluded by an outline describing the aim of every chapter.1.1 Motivation: Enhanced Oil Recovery
1.1.1 Structure and properties of oil reservoirs
Oil and gas originate from geological deposits containing large amounts of organic material, the so‐called source rocks (Figure 1). The material has been converted to oil in a time span of thousands of years by bacterial action and extreme pressures and temperatures. Afterwards, the oil migrated via the pore space between rock or sand grains and ended up in the reservoir rock. This reservoir is a layer of porous and permeable rock (e.g. sandstone or limestone) that contains oil as a single hydraulically connected system. Pore sizes can vary from the submicron to submillimeter scale, and the porosity of the rock, which is the fraction that is not occupied by mineral grains, is approximately 20%. The larger fraction of the pore space is filled with oil, while a minor fraction (one fifth) consists of connate water, which was trapped during rock deposition. Reservoirs are typically a few km long and about 100 m thick, and are located at a depth of a few km. At these depths, elevated pressures (10‐100 MPa) and temperatures (40‐ 200 C) are encountered. The oil is trapped in the reservoir by a seal of impermeable rock. There may be a gas cap above and a water‐bearing permeable rock, an aquifer, below the oil. 1.1.2 Recovering oil reserves Oil reserves are defined as “those quantities of petroleum anticipated to be commercially recoverable by application of development projects to known accumulations from a given date forward under defined conditions” (Petroleum Resources Management System). An important criterion is thus that the oil should be recoverable with existing techniques. The current total reserves are estimated at 200 billion cubic meters, which should be sufficient for 50 years of oil production at the current production rates. Increasing this time span results in more time to fully switch to other energy sources. Besides reducing oil consumption, the location of new oil fields through exploration is an option, however, the opportunities for discovering new oil fields are diminishing. An alternative option is increasing the recovery factor of existing oil fields.
Oil is recovered in various stages. During primary recovery, 5‐15% of the oil initially present in the reservoir rock is produced by making use of natural mechanisms. Oil flows to the drilled production wells due to the high pressure in the reservoir, and is replaced by expanding gas or inflowing water. The flow of oil and water through the rock pore space can thus be considered as an applied two‐phase flow microfluidics problem, which can be
1.1 Motivation: Enhanced Oil Recovery 3 Figure 1 Schematic of an oil reservoir (not to scale). conveniently modeled by two‐phase flows in three‐dimensional bead packs or quasi two‐ dimensional microfluidic devices. During the recovery process the reservoir pressure decreases until it becomes too low for spontaneous oil production. The recovery factor is increased to about 40% by secondary recovery, which involves the pumping of water (or gas) in injection wells to maintain an elevated pressure in the reservoir. However, a large fraction of the oil still remains in the reservoir due to rock heterogeneity, both in wettability and structure. As the less viscous water finds a preferential flow path from the injection well to the production well, significant volumes of oil can be completely bypassed. In addition, oil remains trapped in the pore‐space by capillary forces. Oil production via secondary recovery becomes uneconomical when large amounts of water are produced. Tertiary recovery or Enhanced Oil Recovery (EOR) is a generic term for techniques that are used to further increase the amount of recovered oil. Some examples include reduction of the oil‐water interfacial tension (for example via the addition of surfactant to the water [1], the use of microbes to produce biosurfactant in situ [2], or gas injection [3]), alteration of the wettability of minerals by injection of low salinity water [4], ultrasonic or seismic stimulation [5, 6], addition of polymers to block preferential flow paths and increase the sweep area [7, 8], pulsed or cyclic water injection [9], and hydraulic fracturing [10]. If new EOR techniques can be used to increase the current recovery factor with 10‐20%, this would result in an additional 5‐10 years of oil production and an increased production rate. seal r ock reser voir r ock source rock fault gas water oil oil migraon drilling plaorm
Figure 2 Cross‐section of a sandstone sample observed with SEM, showing quartz and feldspar grains and two forms of clay in the pore space. Picture from K. Dalby [11].
1.1.3 Reservoir complexity
As an example of the above‐mentioned reservoir rock heterogeneity, we will discuss the complexity of a sandstone sample (Figure 2). Sandstone is composed of submillimeter, rounded quartz and feldspar grains with irregular surfaces. The pore space in between the sand grains contains smaller particles of quartz and feldspar, and often clay minerals such as kaolinite, illite, montmorrillonite, muscovite, and chlorite. The clay is also present as a very thin layer on the surface of the sand grains. Oil and water thus mainly interact with clay minerals, which constitute the major part of the surface area of the pores. Besides the inhomogeneity of the reservoir rock, also the pore fluids contribute to a large extent to the complexity of the entire system. Petroleum consists of linear alkanes, naphthenes (cycloalkanes), aromatic hydrocarbons, and the more complex asphaltenes. Besides hydrocarbons, various other organic compounds containing nitrogen, oxygen and sulfur are found. Polar compounds are mainly present amongst the larger molecules and may adsorb to the clay minerals, thereby influencing the effective wettability of the pore space. Both connate water and injection water (often seawater) contain various salts, where NaCl, MgCl2, CaCl2, and KCl are the most abundant. Important properties of the
aqueous phase are the overall salinity, the valency of the cations and the presence of ions with specific effects. 300mm feldspar quartz clay clay
1.1 Motivation: Enhanced Oil Recovery 5
Figure 3 Schematic showing the effect of low salinity water flooding. Switching from a high salinity to a low salinity brine yields a 5‐20% increment in oil recovery.
1.1.4 Low salinity water flooding
It can take over 10 years for a new Enhanced Oil Recovery technique to develop from the research stage to deployment in the field. The effect on residual oil saturation is successively determined in core floods (laboratory test on a formation sample), single well chemical tracer tests (field test near a single wellbore), and interwell trials (field test in between two wellbores). Early work on the effect of brine composition during core floods in sandstone cores was performed by Morrow et al. [12‐15] in the 1990s. The injection of low salinity brine in cores containing clays and crude oil was shown to increases the recovery with up to 15‐40% as compared to high salinity brine. Recently, field trials were performed, initially on clay‐bearing sandstone formations in near wellbore regions [4, 16, 17]. Single well tests performed on the Prudhoe Bay and Endicott fields on the North slope of Alaska showed an increase in oil recovery of 8‐19% when injecting a low salinity (1500 ppm) instead of a high salinity (30000 ppm) brine [4]. Subsequently, interwell tests were executed to unambiguously measure the effect of low salinity water flooding on the field scale, resulting in an incremental recovery of about 10% in the pilot tests (Figure 3) [18]. Various mechanisms have been proposed to explain the effect of low salinity flooding, for example the mobilization of clay fines [15]. Upon contact with low salinity brine, clay particles would detach from the pore surfaces and migrate to the oil‐water interface, thus mobilizing previously retained oil drops. However, migration of fines and the resulting permeability reduction due to blocking of pore constrictions was not observed in
high salinity brine injecon (~ 30 000 ppm) low salinity brine injecon (~ 1 500 ppm)
Pore volumes of water injected (pV)
Oil r e c o v e ry (%) 30-50 % 5-20 % incremental recovery
numerous core floods showing the low salinity effect [19]. Another possible explanation is a rise in pH due to carbonate dissolution and cation exchange. The pH increase would reduce the oil‐water interfacial tension, increase the water wettability of the rock, and lead to in‐situ generation of surfactants by saponification of acid compounds [4]. However, during many low salinity flooding tests low acid numbers and little pH variation were observed [19].
A more recently proposed mechanism for low salinity flooding is multi‐component ion exchange between charged clay particles and the injected brine [19, 20]. In the generally accepted picture the pore space of the reservoir rock was originally filled with water and the pore walls were mostly hydrophilic (i.e. water wet). Upon oil migration from a source rock the smallest pores remained water‐filled, however, in the largest part of the pore space the water was displaced by oil. The pore walls became more hydrophobic (i.e. oil wet) due to adsorption of oil compounds to the rock surface over time. As mentioned before, the pore walls mainly consist of charged clay minerals and silicon. Organic matter and clay minerals can interact via different mechanisms, of which some can be strongly affected by cation exchange (Figure 4). Multivalent cations, such as Mg2+ and Ca2+, can act as bridges between the negatively charged clay surface and negatively charged compounds in the oil phase, either via direct bond formation (ligand bonding) or weak adsorption (cation bridging or water bridging, in the case of solvated cations). Another option is direct adsorption of organic polar compounds onto clay minerals by displacing mobile cations (cation exchange). During low salinity flooding, cations are thought to transfer between the clay minerals and the brine, thereby facilitating removal of organic compounds and organometallic complexes from the rock surface. Expansion of the electric double layer due to the low salt concentration enhances the desorption of polar compounds. The change in wettability to a less oil wet surface would then yield an increased recovery [19, 20].
A pore‐scale model of the low salinity water flooding has been proposed to show the consequences of these wettability changes. The calculations predict the magnitude of the effect semi‐quantitatively: a modest reduction in the oil contact angle of about 10 in the oil wet pores can easily lead to a significant incremental oil recovery of up to 60% [20]. Experimental verification of the exact physical‐chemical mechanisms of wettability alteration is yet to be obtained. As a first step, the stability of Langmuir‐Blodgett layers of stearic acid on silica surfaces is shown to be strongly enhanced by the presence of Ca2+ ions [21].
1.2 Thesis outline 7
Figure 4 Interaction mechanisms between organic matter and clay minerals that can be affected by cation exchange. Figure adapted from Seccombe et al. [17].
1.2 Thesis outline
In this thesis we investigate various aspects related to the mobilization and subsequent removal of liquids interacting with solid walls, on the level of single drops. Oil drops in the rock pore space are in contact with chemically heterogeneous and rough surfaces, resulting in a range of possible local minimum energy configurations separated by energy barriers. Drops can change their shape in a characteristic and typically abrupt manner upon variations in the drop volume or surface wettability to adopt a morphology with lower energy. We review the topic of these so‐called morphological transitions in the theoretical background in Chapter 2. Although the wettability variations in low salinity water flooding are supposedly caused by the desorption of organic compounds, we rely on electrically induced variations in the contact angle. Chapter 2 concludes with a discussion on electrowetting as a method to tune the wettability of substrates continuously and reversibly on very short time scales.
Our experimental investigation starts in Chapter 3 with the effect of adsorption processes. The primary effect triggering enhanced oil recovery in low salinity water flooding is believed to be the alteration of the contact angle, as a consequence of underlying molecular processes such as adsorption, desorption, and assembly of surface active molecules (such as asphaltenes and naphthenates). Besides adsorption onto the rock and clay surfaces, also the adsorption onto the oil‐water interface influences the contact
O-C
Ca
Mg
2+O
O
Ca²⁺
-C
O
O
O
O-C
O
O - H
H ⁺
O-water bridging caon bridging
ligand bonding caon exchange clay oil
R
R
R
O-N⁺
R
R₁
R₂
R₃
angle. Also, the formation of solid layers with a surface viscoelasticity on these interfaces might influence the release of drops in complex natural systems. We study a simplified model system consisting of a linear alkane as the oil phase, containing the interfacially active compound stearic acid, in contact with an aqueous phase. We identify the effect of the composition of the aqueous (water flooding) phase, i.e. the pH, and the type and concentration of the ions, on the formation and composition of three‐dimensional structures of metal stearates on the oil‐water interface.
Chapter 4 discusses the development of a method to monitor the adsorption of surface
active species to an oil‐water interface. A drop of aqueous solution containing a simple surfactant is subjected to electrowetting in an open chip geometry. Analyzing the variation of the contact angle during consecutive amplitude modulations of the voltage yields the interfacial tension as function of drop age. We discuss the time resolution of our technique and the advantages compared to conventional techniques in terms of measured output and sample requirements.
In Chapter 5 and Chapter 6 we focus our attention to morphological transitions induced by wettability variations. The resulting variations in drop‐substrate adhesion and exposure of the drop to external forces facilitate subsequent removal. We study morphological transition in two simplified systems, and use chemically uniform substrates without adsorbed compounds; changes in the effective wettability are obtained via electrowetting. In Chapter 5, a drop confined in between a sphere and a plate is studied. The morphology and radial position of a drop at equilibrium are dependent on the contact angle, drop volume, and sphere‐plate separation. Analysis of the energy landscape shows the occurrence of a symmetry breaking that takes place in the absence of energy barriers and should thus be continuous. To explain the yet observed hysteresis in the shape and position of the drop during the experiments, we numerically study the effect of pinning. We show that small pinning forces can drastically affect the drop behavior, and delay or even preclude the outward movement. A discontinuous transition (without pinning) is observed for a drop on a fiber: the different morphology classes are the so‐called ‘barrel’ engulfing the fiber and the ‘clamshell’ sitting on the side of the fiber. The latter can be more easily detached (and subsequently removed) by external forces. In absence of gravity, the equilibrium shape is determined only by the contact angle and the drop volume, and a large regime can be found in which both shapes are metastable. In Chapter 6 we specifically investigate the effect of buoyancy on the instability lines, introducing an additional length scale (i.e. the capillary
1.2 Thesis outline 9 length) into the problem. We also show the existence of an additional stability limit for the clamshell, introducing (partial) detachment of liquid from the fiber. This ‘release’ cannot be observed without external driving force (like buoyancy or flow). In Chapter 7 we subsequently consider the balance between retaining and driving forces during drop trapping and release. Drops that are trapped in the rock pore space are modeled by drops confined between the top and bottom walls of a simple microfluidic channel. We again make use of electrowetting, now to create a local ‘wetting defect’ with tunable strength. Drops that are trapped by the defect, can be released again by increasing the hydrodynamic driving force. In such a confined environment, the pressure difference over the drop has a larger contribution than the viscous shear stresses in the surrounding fluid. We set up a simple model that predicts whether drops are released from the pinning site. In addition, our approach of incorporating electrodes in microchannel walls offers interesting opportunities in continuous‐flow microfluidics, combining a high throughput with individual drop control.
Finally, we present our overall conclusions and outlook in Chapter 8. We discuss the implications for the forces required for drop removal in (enhanced) oil recovery.
References
[1] W. Xu, S.C. Ayrala and D.N. Rao, Measurement of surfactant‐induced interfacial
interactions at reservoir conditions, SPE Reserv. Eval. Eng. 11 (2008), 83‐94.
[2] S. Maudgalya, R.M. Knapp and M.J. Mcinerney, Microbially enhanced oil recovery
technologies: a review of the past, present and future, SPE Production and Operations
Symposium, Oklahoma City (2007), SPE 106978.
[3] F.I. Stalkup, Status of miscible displacement, J. Pet. Technol. 35 (1983), 815‐826. [4] P.L. Mcguire, J.R. Chatham, F.K. Paskvan, D.M. Sommer and F.H. Carini, Low salinity oil
recovery: An exciting new EOR opportunity for Alaska’s North Slope, SPE Western
Regional Meeting, Irvine (2005), SPE 93902.
[5] M. Hilpert, Capillarity‐induced resonance of blobs in porous media: Analytical
solutions, Lattice‐Boltzmann modeling, and blob mobilization, J. Colloid Interface Sci.
309 (2007), 493‐504.
[6] C. Huh, Improved oil recovery by seismic vibration: A preliminary assessment of
possible mechanisms, First International Oil Conference and Exhibition in Mexico,
Cancun (2006), SPE 103870.
[7] C. Norman, B. Turner, J.L. Romero, G. Centeno and E. Muruaga, A review of over 100
polymer gel injection well conformance treatments in Argentina and Venezuela: Design, field implementation and evaluation, First International Oil Conference and
Exhibition in Mexico, Cancun (2006), SPE 101781.
[8] H. Frampton, J.C. Morgan, S.K. Cheung, L. Munson, K.T. Chang and D. Williams,
Development of a novel waterflood conformance control system, SPE/DOE Fourteenth
Symposium on Improved Oil Recovery, Tulsa (2004), SPE 89391.
[9] D.A. Ivanov and M. Araujo, Dynamics of two‐phase immiscible pulsed flow, SPE/DOE Symposium on Improved Oil, Tulsa (2006), SPE 99678.
[10] B.W. Mcdaniel, Review of current fracture stimulation techniques for best economics
in multilayer, lower‐permeability reservoirs, SPE Eastern Regional Meeting,
Morgantown (2005), SPE 98025.
[11] K. Dalby, personal communication (2014).
[12] P.P. Jadhunandan and N.R. Morrow, Spontaneous imbibition of water by crude‐
oil/brine/rock systems, In Situ 15 (1991), 319‐345.
[13] P.P. Jadhunandan and N.R. Morrow, Effect of wettability on waterflood recovery for
crude‐oil/brine/rock systems, SPE Reserv. Eng. 10 (1995), 40‐46.
[14] H.O. Yildiz and N.R. Morrow, Effect of brine composition on recovery of Moutray crude
References 11
[15] G.Q. Tang and N.R. Morrow, Influence of brine composition and fines migration on
crude oil/brine/rock interactions and oil recovery, J. Pet. Sci. Eng. 24 (1999), 99‐111.
[16] K.J. Webb, C.J.J. Black and H. Al‐Ajeel, Low salinity oil recovery ‐ log‐inject‐log, SPE/DOE Improved Oil Recovery Symposium, Tulsa (2004).
[17] J.C. Seccombe, A. Lager, K.J. Webb, G.R. Jerauld and E. Fueg, Improving waterflood
recovery: LoSal EOR field evaluation, SPE/DOE Improved Oil Recovery Symposium,
Tulsa (2008).
[18] J.C. Seccombe, A. Lager, G.R. Jerauld, B. Jhaveri, T. Buikema, S. Bassler, J. Denis, K.J. Webb, A. Cocking and E. Fueg, Demonstration of low‐salinity EOR at interwell scale,
Endicott Field, Alaska, SPE Improved Oil Recovery Symposium, Tulsa (2010).
[19] A. Lager, K.J. Webb and C.J.J. Black, Low salinity oil recovery ‐ An experimental
investigation, Society of Core Analysts Meeting, Trondheim (2006).
[20] K.S. Sorbie and I.R. Collins, A proposed pore‐scale mechanism for how low salinity
waterflooding works, SPE Improved Oil Recovery Symposium, Tulsa (2010), SPE
129833.
[21] N. Kumar, L. Wang, I. Siretanu, M. Duits and F. Mugele, Salt dependent stability of
stearic acid Langmuir‐Blodgett films exposed to aqueous electrolytes, Langmuir 29
(2013), 5150‐5159.
Chapter 2
Scientific background
Crude oil that is present in a reservoir rock interacts with pore walls with a large degree of complexity; rock grains have variable shapes with irregular surfaces, and the variety in absorbed clay minerals and polar compounds causes microscopic chemical and structural heterogeneity. In this chapter, we discuss the interaction of liquid drops with surfaces that are structured on very different length scales; the structure is either much smaller than or comparable to the drop size. These structured surfaces are particularly interesting because they allow for different drop shapes dependent on the surface wettability or the liquid volume. A decreased drop adhesion and increased exposure to external forces (due to release from confinement) might facilitate subsequent drop removal.We start with a concise overview of the basic concepts of capillarity and wetting that are encountered throughout this thesis, and the wetting of microscopically textured surfaces. An extensive discussion of these two topics can be found in the book ‘Capillarity and Wetting Phenomena’ by de Gennes, Brochard‐Wyart, and Quéré [1], and recent review papers by Quéré [2, 3] and Bonn et al. [4]. Morphological transitions on surfaces structured on the scale of the drop size are subsequently covered; we start with a discussion of general considerations, and continue with some examples of morphological transitions as described in recent literature. In this thesis, we rely on electrically induced variations in the contact angle to study the effect of wettability alterations. Hence, we
2.1 Basic concepts of capillarity and wetting
2.1.1 Surface tension
Small liquid volumes tend to assume a perfectly spherical shape, and surface tension opposes the distortion of the surface by other forces. The physical origin of surface tension is shown in Figure 1A. A molecule that is segregated to the surface loses half its cohesive interactions with the bulk liquid and is thus in an energetically unfavorable state. As creation of new surface is energetically costly fluid systems tend to minimize their surface area. The surface tension is of order ≅ / 2 , with the cohesion energy per molecule and the area of the molecule, and is thus dependent on the type of cohesive force. Oils have a relative low surface tension of 20 mJ/m2 due to van der Waals interactions, while water has a surface tension of 72 mJ/m2 due to hydrogen bonding. An interface between two immiscible liquids is similarly characterized by an interfacial tension, which originates from different attractive intermolecular interactions in the liquids. Surface tension can also be expressed as a force per unit length (mN/m), where the line tension acts in all directions parallel to the surface.
2.1.2 Surfactants
The interfacial tension of a liquid in contact with air, a second liquid or a solid can be reduced by the use of so‐called surfactants, i.e., surface active agents. Surfactants are amphiphilic organic molecules, consisting of a hydrophobic and a hydrophilic group. The hydrophobic group of dissolved surfactants distorts hydrogen bonding between water molecules, thereby restricting their mobility; the driving force for adsorption to the interface is thus an increase of entropy of the solvent molecules. After creation of a fresh interface the interfacial tension gradually decreases from the value of the ‘bare’ interface to the equilibrium interfacial tension. The overall process involves various stages, such as diffusion of the surfactant molecules from the bulk to the interface, and adsorption and re‐orientation at the interface. Figure 1B shows the example of stearic acid, which has a hydrophilic acid group that can dissociate depending on the pH of the solution, and a hydrophobic hydrocarbon tail. Stearic acid is used in Chapter 3 as a simple model compound for the variety of surfactants naturally present in oil reservoirs.
2.1.3 Laplace pressure
The interfacial tension causes a pressure difference between the interior and exterior of a curved interface. In Figure 2 we consider a small section of a liquid interface with principal
2.1 Basic concepts of capillarity and wetting 15 Figure 1 Interfacial tension of a liquid‐vapor interface. (A) Liquid molecules and their cohesive interactions in the bulk and at the interface. (B) Stearic acid (CH3(CH2)16CO2H) is an example of a surfactant that reduces interfacial tension.
Figure 2 Determination of the Laplace pressure by dilating a liquid interface at constant
pressure. Figure adapted from Bruus [6].
radii of curvature and , which is displaced by an amount in the direction normal to the interface, at constant pressure. The work done by the capillary force and pressure is
∆ , where the increase in interfacial area is ≅ 1/ 1/ , and the increase in volume is ≅ . The condition for mechanical equilibrium 0 yields an expression for the Laplace pressure difference
∆ 1/ 1/ 2 , with the mean curvature of the
interface. For spherical drops of radius this reduces to Δ 2 / . The Laplace pressure hence increases for decreasing drop size, and is typically comparable to atmospheric pressure for micron‐sized drops. liquid vapor
O
OH
A Bhydrophilic head group
hydrophobic tail dz dy+d dy z R/ 2 dx+d dx z R/ 1 dx dy R2+dz R2 R1+dz R1
Figure 3 Examples of Delaunay surfaces. (A) Unduloid , , (B) nodoid , , (C) sphere
0, , (D) catenoid , ∞ , and (E) cylinder , . Figure adapted from Baret [7].
2.1.4 Constant mean curvature surfaces
In the absence of external forces, the constant pressure throughout the drop implies a constant mean curvature of the interface, which is a spherical shape for a free liquid volume. For the more general case of axisymmetric liquid volumes with boundary conditions, Delaunay [8] proved that constant mean curvature surfaces are obtained by rotating the roulettes of conics (i.e., parabolic, elliptic, and hyperbolic catenaries). The thus obtained surfaces of revolution are catenoids, unduloids, and nodoids, in addition to the elementary cases of spheres and cylinders, and can be parameterized by the minimal radius and the maximal radius (Figure 3). Although the Delaunay surfaces are periodic surfaces, only portions of these surfaces are physically stable. Unduloids are unstable due to the Rayleigh‐Plateau instability [9], while nodoids are unstable due to the intersecting surface. The necessary boundary conditions are provided by contacting solid substrates, for example in the case of a capillary bridge in between two planes or two spheres. In Chapter 5, we represent small oil volumes in rock pore spaces by the generic geometry of a drop confined between a sphere and a plane. We discuss the symmetry
D E B A C r1 r2
2.1 Basic concepts of capillarity and wetting 17
Figure 4 Competing morphologies of drops on fibers. Profile of a (A) barrel shape and (B)
clamshell shape.
breaking of these liquid bridges with constant mean curvature above a volume‐ and separation‐dependent critical contact angle.
The boundary conditions can also be provided by a cylindrical surface, a ‘fiber’. We first assume that the liquid connects to the fiber surface at zero angle (Figure 4A). At the apex of the drop, both principal radii of curvature are of the order of the drop size , resulting in a mean curvature 1/ . At the outer edge of the drop however, the radius of curvature perpendicular to the plane of the figure becomes very small, i.e., equal to the radius of the fiber ≪ . This implies that the radius of curvature in the plane of the figure should become negative, and the drop profile contains an inflection point. As can be seen in Figure 4A, the liquid surface again takes the shape of a Delaunay surface (unduloid), as expected for a cylindrically symmetric drop. Upon changing the angle between the liquid interface and the fiber surface, the so‐called ‘barrel’ shape [10, 11] competes with a second constant mean curvature shape, the symmetry‐broken ‘clamshell’ morphology (Figure 4B). Which of these morphologies is attained also depends on the volume of the drop and the history of the system [12].
2.1.5 Capillary length
While the interfacial tension tends to minimize the interfacial area of a drop, deformations in the shape can be induced by external forces. One can define the capillary length /Δ , which is a characteristic length comparing the effects of interfacial tension and buoyancy. The capillary length is typically a few millimeters for liquid‐vapor interfaces. For drops much smaller than , the surface force due to interfacial tension dominates the body force from gravitational acceleration, and a mean curvature shape is attained. In case of liquid/ liquid systems, the capillary length can be drastically increased
via density matching of both liquid phases. For drops larger than , buoyancy effects
should be taken into account. In Chapter 6 we investigate the influence of buoyancy
A B
Figure 5 Determination of the Young angle via (A) energy or (B) force considerations.
forces on the morphological transitions of drops on fibers (Figure 4). Varying the mass density of the ambient phase allows for tuning of the capillary length in a broad range.
2.1.6 Young angle
When a liquid volume is placed on a chemically and topographically homogeneous planar surface, it either spreads completely or forms a liquid lens. In the latter case, the three phases that need to be considered – i.e., the solid phase ( ), the liquid phase ( ), and the vapor (or a second, immiscible liquid) phase ( ) – coexist at the three phase contact line, where the liquid‐vapor interface makes an angle with the surface. This Young angle can be derived by calculating the variation of the interfacial energy associated with a small reversible change in contact line position (Figure 5A). The variation is given by cos , with , , and the solid‐vapor, solid‐liquid, and liquid‐vapor interfacial tension, respectively. In thermodynamic equilibrium the energy change is zero, which results in the Young relation cos / . The contact angle is thus determined by the chemical nature of the three phases. Alternatively, the Young angle can be derived from a balance between the equilibrium forces, i.e., the interfacial tensions, in the horizontal direction at the three phase contact line (Figure 5B). The vertical components are responsible for deformations of liquid and soft solid substrates.
These global energy arguments yield the macroscopic contact angle. In the immediate vicinity of the three phase contact line, the slope of the liquid‐vapor interface can deviate from the one described by the Young relation. At distances up to typically a few nanometers from the solid substrate, the local contact angle is affected by the disjoining pressure. Even closer to the surface, on a molecular scale, the interface position is no
A vapor co s d θY x liquid solid dx B θY θY γ γsv γsl
2.1 Basic concepts of capillarity and wetting 19
longer uniquely determined due to thermal fluctuations and interface diffusiveness. However, in this thesis, we are only interested in the macroscopic contact angle.
2.1.7 Spreading parameter
Depending on the values of the interfacial tensions two wetting regimes can be distinguished that can be characterized by the spreading parameter , which compares the difference in interfacial energies of the dry and wet substrate. For 0, the energy of the system is minimized by complete wetting; the solid substrate is covered by a nanoscopic uniform liquid layer, of which the thickness is set by a competition between capillary forces and long range intermolecular forces (van der Waals interactions). Complete wetting is promoted by high‐energy surfaces with large chemical binding energies, for low interfacial tension liquids such as light alkanes and silicon oils, and by the use of surfactants. For 0, the energy of the system is minimized by a drop with a finite contact angle satisfying the Young relation. The partial wetting regime is shown on low‐energy surfaces, and can be divided in ‘preferentially wetting’ for contact angles smaller than /2 (also called hydrophilic in case of water drops) and ‘preferentially non‐wetting’ for contact angles larger than /2 (hydrophobic). An interesting limit is found for 2 , for which the drop is in a complete non‐wetting situation. Complete non‐wetting is highly desired for easy drop removal, and can be achieved in oil‐water systems via complete wetting of the ambient phase. 2.1.8 Contact angle hysteresis The derivation of the Young angle in Section 2.1.6 is based on the assumption of an ‘ideal’ surface, i.e., a planar substrate that is both chemically and topographically homogeneous. However, real surfaces are non‐ideal due to small chemical (i.e., wettability) and physical defects. Due to these nanometric to micrometric heterogeneities, the contact angle is not uniquely defined. An example of such a defect is a sharp edge (Figure 6A), where the apparent angle between the liquid‐vapor interface and the horizontal increases from to , before the contact line proceeds. The dissipation upon depinning of the contact line is the fundamental mechanism of contact angle hysteresis.
Pinning of the contact line by small heterogeneities introduces an additional horizontal force that opposes the motion of the contact line (Figure 6B). As a result the contact line only advances (recedes) as soon as the advancing (receding) contact angle ( ) is reached. The contact angle hysteresis is defined as the difference between these two angles, and the threshold force required to move a drop on such a surface is
Figure 6 (A) On a sharp edge the apparent contact angle can assume any value between and
. (B) Due to contact line pinning, the apparent contact angle can assume any value between the receding and the advancing contact angle.
proportional to ∆ cos cos cos . ‘Good’, i.e., clean and microscopically flat, substrates have a contact angle hysteresis smaller than 5. The hysteresis of rough or dirty substrates, such as rock surfaces, is typically several tens of degrees, and can even become comparable to the advancing angle.
2.2 Wetting of microscopically textured surfaces
We now first consider the interaction of liquids with surfaces that are textured on scales much smaller than the drop size. The surface properties are dependent on roughness and wettability variations, i.e., on the spatial variations in the geometry and the chemical properties. The presence of these defects not only results in contact angle hysteresis, but also affects the apparent contact angle and can induce different drop regimes.
2.2.1 Wenzel and Cassie‐Baxter models
The apparent contact angle ∗ reflects the average properties of the substrate in the proximity of the contact line. For both topographically heterogeneous (structured) and chemically heterogeneous (patterned) surfaces, we are interested in ∗ as a function of the Young angle and the other parameters characterizing the substrate. A small displacement of the contact line parallel to the surface yields a change in surface energy. This variation is set to zero to find the equilibrium apparent contact angle.
A structured surface is characterized by its roughness factor 1, where is the ratio of the actual surface area over the apparent one (Figure 7A). When the liquid follows all topological variations of the material, we find the Wenzel relation cos ∗ cos . Surface roughness hence always ‘magnifies’ the underlying wetting properties. A
Fp A B θ θ ψ π ψ θ- + γ γsv γsl θ θ θr< < a
2.2 Wetting of microscopically textured surfaces 21
Figure 7 Edge of a drop placed on a (A) rough surface, yielding the Wenzel relation, and on a
(B) chemically heterogeneous surface, yielding the Cassie‐Baxter relation.
patterned surface consisting of two species with different wettability (Figure 7B) is characterized by the fractional surface areas of both species 1 and their respective contact angles and . The apparent contact angle is then given by the Cassie‐Baxter relation cos ∗ cos cos , i.e., it is obtained from a weighted average of the cosines of the angles of both species.
2.2.2 Superhydrophilic and superhydrophobic surfaces
The Wenzel relation predicts a critical roughness factor 1/|cos | at which complete wetting or complete drying is attained. However, the Wenzel model is only valid for moderate roughness factors, and hence these regimes cannot be induced by structuring of a surface. In the case of a very rough hydrophilic surface, part of the liquid will fill the microstructure. Drops spreading onto this impregnated state thus encounter a composite substrate with a solid and a liquid fraction (Figure 8A). For very rough hydrophobic surfaces, the liquid does not conform to the asperities of the substrate. Instead, air can remain trapped inside the structure, such that the drop sits on a composite substrate with a solid and a vapor fraction (Figure 8B). Drops deposited on either of these surfaces will thus have an apparent contact angle according to the Cassie‐Baxter relation. Although liquid impregnation and air entrapment enhance hydrophilicity and hydrophobicity, respectively, the drop always partially contacts the solid substrate and is hence in the partial wetting regime. On superhydrophobic surfaces, the contact area with air can be increased by using a low solid fraction 0.1, resulting in an extremely low hysteresis and thus a large drop mobility. A B vapor liquid solid dx co s d θY x co s d θY x dx θ* θ* θ1 θ2
Figure 8 Wenzel and Cassie‐Baxter regimes. In case of (A) superhydrophilic and (B)
superhydrophobic surfaces, the liquid spreads on a composite surface. (C) Apparent contact angle as function of the Young angle for a pillared substrate with 0.25 and 4. The solid lines are based on the energy minimum, while the dotted line indicates the metastable Cassie‐ Baxter regime. 2.2.3 Coexisting states The energies of drops that are satisfying either the Wenzel or the Cassie‐Baxter relation can be compared to find the critical contact angle cos 1 / separating both regimes. Figure 8C summarizes the results for a simple structured surface with well‐ defined pillars and without chemical heterogeneity. For hydrophilic surfaces, a large roughness implies a large and thus promotes liquid impregnation. For hydrophobic surfaces, a large roughness implies a small and thus promotes air entrapment.
The description of the superhydrophobic state is complemented by the necessary condition to satisfy the Young relation at all contact lines, i.e., at the edge of the drop and for each liquid‐vapor interface below the drop. The pinning of the contact line on sharp edges (Figure 6A) introduces an energy barrier ≫ , and a metastable Cassie‐Baxter regime for contact angles smaller than . Under these conditions, careful deposition of liquid results in a Cassie‐Baxter drop, while vapor condensation yields a Wenzel drop with significantly smaller contact angle and larger contact angle hysteresis. This metastable Cassie‐Baxter state is fragile; a transition to the lower energy Wenzel state can be easily induced by increasing the pressure. Impalement occurs either via depinning of the contact lines as soon as the angle of the liquid‐vapor interfaces with respect to the vertical wall exceeds the Young angle, or via nucleation of solid‐liquid contact on the bare substrate. B dx A vapor liquid solid dx We nze l re gim e C-B regime: liquid impregnaon C-B regime: air entrapment C θ* θ*
